{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7UTPN2FMICPBPLFQHT53KZL354","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"943ae0bbdf5587f246e04362df1b617e91f28488d335c8a99c60de0a3b19edb0","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-07-07T09:21:18Z","title_canon_sha256":"5b719b3c9d0f2d62f4913afe78052cad31109bc175800f1c78b9a1c1ba1bd5e2"},"schema_version":"1.0","source":{"id":"1707.02871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02871","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02871v1","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02871","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"pith_short_12","alias_value":"7UTPN2FMICPB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7UTPN2FMICPBPLFQ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7UTPN2FM","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:8d504baec73a03ddad9cd4e1691f44d6ef007eb817fb4a965916bad7a6e042b2","target":"graph","created_at":"2026-05-18T00:40:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof of his result. Our approach allows us to give an explicit bound for this kind of fair division. Furthermore, we also give a theoretical answer to an open problem posed by Barbanel in 1996. Roughly speaking, this question is: how can we decide if there exists a fair division satisfying some inequalities constraints? Furthermore, when all the measures are given with piecewise constant density functions then we show ho","authors_text":"Guillaume Ch\\`eze (IMT), Luca Amodei (IMT)","cross_cats":["cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-07-07T09:21:18Z","title":"How to cut a cake with a gram matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02871","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:992bc04dc90b99a7902cffe4ec0ea3d323f34f03f621958a8d9bccb0a31447f4","target":"record","created_at":"2026-05-18T00:40:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"943ae0bbdf5587f246e04362df1b617e91f28488d335c8a99c60de0a3b19edb0","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-07-07T09:21:18Z","title_canon_sha256":"5b719b3c9d0f2d62f4913afe78052cad31109bc175800f1c78b9a1c1ba1bd5e2"},"schema_version":"1.0","source":{"id":"1707.02871","kind":"arxiv","version":1}},"canonical_sha256":"fd26f6e8ac409e17acb03cfbb5657bef2e85ac654469d0f4b95c753143c59e32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd26f6e8ac409e17acb03cfbb5657bef2e85ac654469d0f4b95c753143c59e32","first_computed_at":"2026-05-18T00:40:35.554210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:35.554210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c/kkr5ro7zN1opdNJ1CU+RfXnrBh9q1jOt9zI0KIGptX3hMGIvMVGEk8ruAr2gMdmqaFJ6XJ7RvawxIUXWwBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:35.554864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:992bc04dc90b99a7902cffe4ec0ea3d323f34f03f621958a8d9bccb0a31447f4","sha256:8d504baec73a03ddad9cd4e1691f44d6ef007eb817fb4a965916bad7a6e042b2"],"state_sha256":"d59f65d670c4c5ee578f673b89722c46078666bed2c4944d0ba9028ffb25e24f"}